Parallel Algorithms for Burrows-Wheeler Compression and Decompression

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Abstract

We present work-optimal PRAM algorithms for Burrows-Wheeler compression
and decompression of strings over a constant alphabet. For a string of
length n, the depth of the compression algorithm is O(log2 n), and the depth
of the the corresponding decompression algorithm is O(log n). These appear
to be the first polylogarithmic-time work-optimal parallel algorithms for any
standard lossless compression scheme.
The algorithms for the individual stages of compression and decompression
may also be of independent interest: 1. a novel O(log n)-time, O(n)-work
PRAM algorithm for Huffman decoding; 2. original insights into the stages of
the BW compression and decompression problems, bringing out parallelism
that was not readily apparent, allowing them to be mapped to elementary
parallel routines that have O(log n)-time, O(n)-work solutions, such as: (i)
prefix-sums problems with an appropriately-defined associative binary operator
for several stages, and (ii) list ranking for the final stage of decompression.